Two-state model of acto-myosin attachment-detachment predicts C-process of sinusoidal analysis

Bradley M. Palmer, Takeki Suzuki, Yuan Wang, William D. Barnes, Mark S. Miller, David W. Maughan

Research output: Contribution to journalArticle

Abstract

The force response of activated striated muscle to length perturbations includes the so-called C-process, which has been considered the frequency domain representation of the fast single-exponential force decay after a length step (phases 1 and 2). The underlying molecular mechanisms of this phenomenon, however, are still the subject of various hypotheses. In this study, we derived analytical expressions and created a corresponding computer model to describe the consequences of independent acto-myosin cross-bridges characterized solely by 1), intermittent periods of attachment (tatt) and detachment (tdet), whose values are stochastically governed by independent probability density functions; and 2), a finite Hookian stiffness (k stiff) effective only during periods of attachment. The computer-simulated force response of 20,000 (N) cross-bridges making up a half-sarcomere (Fhs(t)) to sinusoidal length perturbations (L hs(t)) was predicted by the analytical expression in the frequency domain, (F̃hs(ω)/L̃hs(ω)) = (t̄att/t̄cycle)Nk̄stiff(iω /(t̄att-1 + iω)); where t̄att = mean value of tatt, t̄cycle = mean value of t att + tdet, k̄stiff = mean stiffness, and ω = 2π x frequency of perturbation. The simulated force response due to a length step (Lhs) was furthermore predicted by the analytical expression in the time domain, Fhs(t) = (t̄att/ t̄cycle)Nk̄stiffLhs e -t/t̄att. The forms of these analytically derived expressions are consistent with expressions historically used to describe these specific characteristics of a force response and suggest that the cycling of acto-myosin cross-bridges and their associated stiffnesses are responsible for the C-process and for phases 1 and 2. The rate constant 2πc, i.e., the frequency parameter of the historically defined C-process, is shown here to be equal to t̄att-1. Experimental results from activated cardiac muscle examined at different temperatures and containing predominately α- or β-myosin heavy chain isoforms were found to be consistent with the above interpretation.

Original languageEnglish (US)
Pages (from-to)760-769
Number of pages10
JournalBiophysical Journal
Volume93
Issue number3
DOIs
StatePublished - Aug 2007

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pioglitazone
Myosins
Sarcomeres
Striated Muscle
Myosin Heavy Chains
Computer Simulation
Myocardium
Protein Isoforms
Temperature

ASJC Scopus subject areas

  • Biophysics

Cite this

Two-state model of acto-myosin attachment-detachment predicts C-process of sinusoidal analysis. / Palmer, Bradley M.; Suzuki, Takeki; Wang, Yuan; Barnes, William D.; Miller, Mark S.; Maughan, David W.

In: Biophysical Journal, Vol. 93, No. 3, 08.2007, p. 760-769.

Research output: Contribution to journalArticle

Palmer, Bradley M. ; Suzuki, Takeki ; Wang, Yuan ; Barnes, William D. ; Miller, Mark S. ; Maughan, David W. / Two-state model of acto-myosin attachment-detachment predicts C-process of sinusoidal analysis. In: Biophysical Journal. 2007 ; Vol. 93, No. 3. pp. 760-769.
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abstract = "The force response of activated striated muscle to length perturbations includes the so-called C-process, which has been considered the frequency domain representation of the fast single-exponential force decay after a length step (phases 1 and 2). The underlying molecular mechanisms of this phenomenon, however, are still the subject of various hypotheses. In this study, we derived analytical expressions and created a corresponding computer model to describe the consequences of independent acto-myosin cross-bridges characterized solely by 1), intermittent periods of attachment (tatt) and detachment (tdet), whose values are stochastically governed by independent probability density functions; and 2), a finite Hookian stiffness (k stiff) effective only during periods of attachment. The computer-simulated force response of 20,000 (N) cross-bridges making up a half-sarcomere (Fhs(t)) to sinusoidal length perturbations (L hs(t)) was predicted by the analytical expression in the frequency domain, (F̃hs(ω)/L̃hs(ω)) = (t̄att/t̄cycle)Nk̄stiff(iω /(t̄att-1 + iω)); where t̄att = mean value of tatt, t̄cycle = mean value of t att + tdet, k̄stiff = mean stiffness, and ω = 2π x frequency of perturbation. The simulated force response due to a length step (Lhs) was furthermore predicted by the analytical expression in the time domain, Fhs(t) = (t̄att/ t̄cycle)Nk̄stiffLhs e -t/t̄att. The forms of these analytically derived expressions are consistent with expressions historically used to describe these specific characteristics of a force response and suggest that the cycling of acto-myosin cross-bridges and their associated stiffnesses are responsible for the C-process and for phases 1 and 2. The rate constant 2πc, i.e., the frequency parameter of the historically defined C-process, is shown here to be equal to t̄att-1. Experimental results from activated cardiac muscle examined at different temperatures and containing predominately α- or β-myosin heavy chain isoforms were found to be consistent with the above interpretation.",
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